A multiple scattering theory for elastic wave propagation in a discrete random medium is presented. A self‐consistent multiple scattering formalism using theTmatrix of a single scatterer in conjunction with the quasicrystalline approximation (QCA) and a self‐consistent pair correlation function is employed to study the phase velocity and coherent attenuation of elastic waves by a random distribution of cavities and elastic inclusions embedded in an elastic matrix. Both uniform and Gaussian size distributions are assumed. The theoretical results obtained in this study are shown to be in excellent agreement with experimental observations.